Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-02T18:19:05.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Perturbation Bounds and Condition Numbers for a Complex Indefinite Linear Algebraic System

Part of: Numerical analysis: Ordinary differential equations Numerical linear algebra Nonlinear algebraic or transcendental equations

Published online by Cambridge University Press:  12 May 2016

Lei Zhu ,
Wei-Wei Xu  and
Xing-Dong Yang
Lei Zhu*
Affiliation:
College of Engineering, Nanjing Agricultural University, Nanjing 210031, P.R. China
Wei-Wei Xu
Affiliation:
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China
Xing-Dong Yang
Affiliation:
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China
*
*Corresponding author. Email address:[email protected] (L. Zhu)
Get access

Abstract

We consider perturbation bounds and condition numbers for a complex indefinite linear algebraic system, which is of interest in science and engineering. Some existing results are improved, and illustrative numerical examples are provided.

Keywords

Complex indefinite linear algebraic systemperturbation boundscondition numbers

MSC classification

Secondary: 65F10: Iterative methods for linear systems 65F15: Eigenvalues, eigenvectors 65H10: Systems of equations 65L15: Eigenvalue problems
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 2 , May 2016 , pp. 211 - 221
Copyright
Copyright © Global-Science Press 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bai, Z.Z., Optimal parameters in the HSS-like methods for saddle-point problems, Num. Linear Algebra Appl. 16, 447–479 (2009).Google Scholar
[2]Bai, Z.Z., Benzi, M. and Chen, F., On preconditioned MHSS iteration methods for complex symmetric linear systems, Num. Algor. 56, 297–317 (2011).CrossRefGoogle Scholar
[3]Hiptmair, R., Finite elements in computational electromagnetism, Acta Numer. 11, 237–339 (2003).Google Scholar
[4]Bai, Z.Z., Benzi, M. and Chen, F., Modified HSS iteration methods for a class of complex symmetric linear systems, Computing 87, 93–111 (2010).CrossRefGoogle Scholar
[5]Bai, Z.Z., Golub, G.H. and Pan, J.Y., Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems, Num. Math. 98, 1–32 (2004).Google Scholar
[6]Poirier, B., Efficient preconditioning scheme for block partitioned matrices with structured sparsity, Num. Linear Algebra Appl. 7, 715–726 (2000).3.0.CO;2-R>CrossRefGoogle Scholar
[7]Benzi, M. and Bertaccini, D., Block preconditioning of real-valued iterative algorithms for complex linear systems, IMA J. Numer. Anal. 28, 598–618 (2008).CrossRefGoogle Scholar
[8]Feriani, A., Perotti, F. and Simoncini, V., Iterative system solvers for the frequency analysis of linear mechanical systems, Comp. Methods Appl. Mech. Eng. 190, 1719–1739 (2000).CrossRefGoogle Scholar
[9]Freund, R.W., Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Stat. Comp. 13, 425–448 (1992).Google Scholar
[10]Sommerfeld, A., Partial Differential Equations, Academic Press (1949).Google Scholar
[11]Axelsson, O. and Kucherov, A., Real valued iterative methods for solving complex symmetric linear systems, Num. Linear Algebra Appl. 7, 197–218 (2000).3.0.CO;2-S>CrossRefGoogle Scholar
[12]Guo, X.X. and Wang, S., Modified HSS iteration methods for a class of non-Hermitian positive-definite linear systems, Appl. Math. Comput. 218, 10122–10128 (2012).Google Scholar
[13]Xu, W.W. and Li, W., New perturbation analysis for generalized saddle point systems, Calcolo 46, 25–36 (2009).Google Scholar
[14]Chen, X.S., Li, W. and Ng,, M.K.On condition numbers of the spectral projections associated with periodic eigenproblems, J. Comp. Appl. Math. 272, 417–429 (2014).Google Scholar
[15]Xie, Z.J., Li, W. and Jin, X.Q., On condition numbers for the canonical generalized Polar decomposition of real matrices, Electr. J. Linear Algebra. 26, 842–857 (2013).Google Scholar